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Comment Re:Why 2^n-1 (Score 2) 254

It is far easier to test Mersenne numbers for primality than general integers, thanks to the Lucas-Lehmer primality test. Weeding out composite Mersenne numbers by trial factoring is also faster, thanks to a theorem that eliminates most of the candidate factors.

As for numbers of the form 2^n+1, it's easy to show that if 2^n+1 is prime, then n must be a power of two. Such numbers are known as Fermat numbers, and there is also a fast primality test (Pepin's test) for numbers of this form. But because of the power of two in the exponent, each Fermat number is double the size (in terms of the number of digits) of the previous one. It doesn't take long before you exceed current computing capabilities. And so far, all the Fermat numbers we've managed to test have turned out to be composite, apart from the first five. Furthermore, it is conjectured that there are only finitely many Fermat primes, so it's possible we've already found them all. On the other hand, it is conjectured that there are infinitely many Mersenne primes.

Open Source

Broadcom Releases Source Code For Drivers 350

I'm Not There (1956) writes "Broadcom, the world's largest manufacturer of Wi-Fi transceivers, open sources its Linux device drivers. This is a big win for Linux users, as there are a lot of users that face Wi-Fi problems when they use Linux on their laptops. With these device drivers now open source, distributions can ship them out-of-the-box, and that means no Linux Wi-Fi problems for new devices and upcoming distributions at all."
Android

Droid X Self-Destructs If You Try To Mod 757

An anonymous reader writes with some discouraging news for hack-oriented purchasers of the new Droid X phone: "If the eFuse fails to verify [the firmware information (what we call ROMS), the kernel information, and the bootloader version], then the eFuse receives a command to 'blow the fuse' or 'trip the fuse.' This results in the booting process becoming corrupted, followed by a permanent bricking of the phone. This FailSafe is activated anytime the bootloader is tampered with or any of the above three parts of the phone has been tampered with."
Media

IEEE Working Group Considers Kinder, Gentler DRM 236

slave5tom writes "An IEEE working group is trying to put the genie back in the bottle. Its scheme will allow unlimited copying of encrypted content, which will require a playkey to activate. Trying to add a cost by making the playkey 'rivalrous' (what you take I lose) and rescuing the big content players from the brink of oblivion does seem futile, but it is entertaining to watch them fight the inevitable."

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